How do I find the closest possible sum of an Array's elements to a particular value?

Question

In Java, how should I find the closest (or equal) possible sum of an Array\'s elements to a particular value K?

For example, for the array {19,23,41,5,40,36} and K=4

Answer 1

You can see it as a n-choose-k problem for all possible k so the complexity is exponential.

1. Find a set of numbers that sum at most up to K. The set should include i numbers, for i=1; i<=N; i++. To implement this, for each i just take all the n-choose-i combinations of the numbers in the array.
2. Keep a finalResult variable with the best set of numbers found so far and their sum.
3. Compare each sub-result of step 1 with the finalResult and update it if necessary.

It reminds me of the Knapsack problem, so you may want to take a look at it.